On several local asymptotic properties for fractional autoregressive models with strong mixing noises

Abstract

This paper is devoted to study several local asymptotic properties for fractional autoregressive models with strong mixing noises, we treat local asymptotic normality using Swensen’s lemma, then we deal with local asymptotic minimaxity and local asymptotic linearity, these properties are fundamental and prepare the way for the construction of adaptive estimator. In order to measure the performance of our approach we deal with simulation study, it allows us to check the validity of the theoretical results.

Keywords:

• Fractional autoregressive process
• Local asymptotic linearity
• Local asymptotic minimaxity
• Local asymptotic normality
• Strong mixing

Acknowledgements

We acknowledge the support of” Direction Générale de la Recherche Scientifique et du Développement Technologique DGRSDT”.MESRS ALGERIA.